Physics 7B Lecture 718-Feb-2010 Slide 1 of 36
Physics 7B-1 (C/D)Professor Cebra (Guest Lecturer)
Review of Linear Momentum
AndRotational Motion
Winter 2010Lecture 7
Physics 7B Lecture 718-Feb-2010 Slide 2 of 36
Slides 3-19 were discussed in the 7:30 Lecture
Slides 6-27 were discussed in the 9:00 Lecture
Momentum Choose: Which would you
rather be hit by? A tennis ball going 1m/s or a tennis ball going 10m/s. Which would transfer more momentum to you?
Choose: Which would you rather be hit by? A train going 1 m/s or a tennis ball going 1 m/s. Which would transfer more momentum to you?
Momentum is proportional to the mass and the velocity of an object
Momentum has direction and therefore is a vector!
pmv
v
v
v
v
Momentum and Impulse Q: How would you give
an object momentum?
We must apply a force for a given amount of time. The greater the force, the greater the change in momentum. The longer we apply the force, the greater the change in momentum.
A change in momentum is called an impulse J
Momentum has direction and therefore is a vector! Impulse is also a vector.
p Ft
F p
tdp
dt
J Ft
F=1N
Δt=.1s
Q: Find the impulse the player gives to the ball. If the mass of the basketball is 0.5 kg, what is the speed the ball leaves the player’s hand with?
Conservation of Momentum The other big law after
conservation of Energy.
Q: If there is a system with no external force acting upon it, what is the change in momentum of the system?
F 0p 0
pbefore pafter
Q? Will the boat move?
Q: Take a compressed fuel rocket. Which fuel would be better for this rocket, water or air?Q: Why does the tank feel a recoil?
Collisions:Type of Collision
Description Example Momentum(ptot)
Kinetic Energy (Ketot)
Elastic Perfectly bounce off each other – no deformation
Billiard Balls
Conserved Conserved
Inelastic Bounce with some Deformation
Tennis Balls
Conserved Not Consv’d
Perfectly Inelastic
Stick to each other Play-dohBalls
Conserved Not Consv’d
BEFORE AFTER
v8=0vC=8m/s vC=?
m=0.16kgm=0.17kg
v8=?
v2=0v1=10m/s v1=?
m=0.05kgm=0.05kg
v2=?
v2=0v1=10m/s
m=0.1kgm=0.1kg
v1+2=?m=0.2kg
Elastic
Inelastic
Perfectly Inelastic
Q: An astronaut is
performing a spacewalk
when his tether breaks. He
happens to be holding a
1kg tool. Because the
astronaut was paying
attention in his physics
class, he knows that he
can use conservation of
momentum to his
advantage. How?
Q: An astronaut is performing a spacewalk when his tether breaks. He happens to be holding a 1kg tool. Because the astronaut was paying attention in his physics class, he knows that he can use conservation of momentum to his advantage. How?
He can manage to throw the tool at 10m/s
If the astronaut is 10m away from the space shuttle and his mass is 100kg, find the time it takes for him to get back to the Space Shuttle.
Physics 7B Lecture 718-Feb-2010 Slide 9 of 36
The Definition of Impulse
Recall that work was resulted in a change in energy, where work is
f
i
x
xif EEExdxFW
)(
We can similarly define a quantity called the impulse, which is the time integral o f the applied force
f
i
t
tif pppdttFJ
)(
J is a vector quantity, which is applied to the vector p.
Physics 7B Lecture 718-Feb-2010 Slide 10 of 36
Conservation of Momentum
systemifextextext pppdttFJJNet
)(
If the net external impulse in a given direction acting on the system is zero, then there is no change in the linear momentum of the system in that direction; Otherwise there is a change in the momentum equal to the net external impulse.
Conservation of Momentum!
Compare to conservation of Energy
Physics 7B Lecture 718-Feb-2010 Slide 11 of 36
Rockets
Consider a model rocket. How high will a 0.2 kg model rocket fly if your install a class “C” Estes rocket engine? An Estes “C” engine provide 8.0 Newton-seconds of impulse.
msmsmgvh
mvmgh
KEPE
smkgNsv
vkgvmpJ
80)/10/()/1600)(5.0(/)2/1(
)2/1(
/40)2.0/()8(
))(2.0(
2222
2
Physics 7B Lecture 718-Feb-2010 Slide 12 of 36
Collisions
A collision occurs when two free bodies make contact. The contact results in a repulsive normal force. The magnitude of the force and the duration of the contact will determine the resulting impulse. Newton’s 3rd law indicates that each of the two participating bodies will experience an equal but opposite impulse.
All collisions conserve both energy and momentum, however we classify collisions as being either elastic on inelastic based upon whether kinetic energy is conserved.
Elastic collisions conserve both momentum and kinetic energy.
In an inelastic collision some of the energy of the collisions is dissipated as internal energy within the bodies.
In a completely inelastic collision, the two bodies stick together and there is only center of mass motion remaining after the collision
Physics 7B Lecture 718-Feb-2010 Slide 13 of 36
1D Elastic Collisions
Elastic Collisions:
ftotitot
fi
pp
KEKE
,,
Try cases of:• m1=m2 •M1=2m2• m1=(1/2)M2• v1>v2• v1<v2
Demo: collision table
Physics 7B Lecture 718-Feb-2010 Slide 14 of 36
1D Inelastic Collisions
Demo: collision table
Try cases of:Equal masses• m1=m2 •M1=2m2• m1=(1/2)M2• v1>v2• v1<v2
ftotitot
fi
pp
KEKE
,,
Inelastic Collisions:
Physics 7B Lecture 718-Feb-2010 Slide 15 of 36
A Particle Physics Collision
Is this an elastic on inelastic collision?
Physics 7B Lecture 718-Feb-2010 Slide 16 of 36
Inelastic Collisions
Why do cars have crumple zones?
Consider an older model car with a 5 cm bumper and a rigid frame.
Compare to a more model car with a 25 cm crumple zone.
Physics 7B Lecture 718-Feb-2010 Slide 17 of 36
2D Collisions
Demo: Air puck
Must conserve Px and Py
Elastic collisions conserve kinetic energy
When m1=m2, then the angle between p1 and p2
will be 90 degree.
Physics 7B Lecture 718-Feb-2010 Slide 18 of 36
2D Collisions
Where will the cue ball end up?
Where do you aim the 1 (yellow) with respect to the 9 (yellow stripe)?
Physics 7B Lecture 718-Feb-2010 Slide 19 of 36
2D Collisions
Can the American Curling team knock out both the yellow stones?
Where should they aim their stone?
Physics 7B Lecture 718-Feb-2010 Slide 20 of 36
Rotational Motion
Can an object be continually accelerating without gaining any speed?
If the force is always perpendicular to the direction of the velocity, then only the direction changes.
“centripetal acceleration”
v = 2pr/T
r
v
t
va
r
tv
v
v
c
2
Physics 7B Lecture 718-Feb-2010 Slide 21 of 36
Rotational Motion
F
P
Centripetal ForceFc = mac=mv2/r
Spin the ball, then let it go. Due to conservation of momentum, it must go in the straight line Demo: Ball on a string
Physics 7B Lecture 718-Feb-2010 Slide 22 of 36
How fast must the roller coaster be going so that the riders still feel a 0.5 g force even at the top of the 10 meter radius loop-the-loop?
Fc = (3/2)mg = mv2/r
v2 = (3/2)rg = (3/2)(10)(10)
v = 12.2 m/s = 27.5 mph
What provides the centripetal force?
Centripetal Force
Physics 7B Lecture 718-Feb-2010 Slide 23 of 36
Centripetal Force
What is the centripetal force needed to keep the NASCAR 1000 kg cars on the track when taking an R = 200 m curve at 200 mph (320 km/hour)?
F = mv2/r= (1000)(88.9)2/200
= 3.95x104 N
What provides this centripetal force?
rgv
mg
rmv
F
F
r
mvFF
N
N
Nc
/tan
/
cos
sin
sin
2
2
2
Physics 7B Lecture 718-Feb-2010 Slide 24 of 36
Centripetal Force
How far above the surface of the earth must one launch a communications satellite to achieve an geosynchronous orbit?
r = 42,164 km
Note RE = 6378 km
=> Launch altitude above 36000 km
Note also, low earth orbit is anything less than 200 km above the surface of the earth
What provides the centripetal force? GM
rT
T
r
r
GMv
rmvr
mMGFc
2/3
2
2
2
2
/
p
p
Physics 7B Lecture 718-Feb-2010 Slide 25 of 36
Angular Quantities
• There is an analogy between objects moving along a straight path and objects moving along a circular path.
Position ↔ Angle
Velocity ↔ Angular Velocity
Acceleration ↔ Angular Acceleration
Momentum ↔ Angular Momentum
Force ↔ Torque
Physics 7B Lecture 718-Feb-2010 Slide 26 of 36
Angular Velocity
• How do we represent the motion of a rotating disk?
v
Demo: Accelerometer
Physics 7B Lecture 718-Feb-2010 Slide 27 of 36
Angular Velocity
• Angular velocity is a vector:
– Right hand rule to determines direction of ω
– Velocity and radius determine magnitude of ω
r
v
Physics 7B Lecture 718-Feb-2010 Slide 28 of 36
Angular Velocity
• What’s the angular velocity of a point particle?
sinr
v
r
v
v
r┴
r
θ
Physics 7B Lecture 718-Feb-2010 Slide 29 of 36
Angular Acceleration
• Angular Acceleration: Rate of change in angular velocity
• A stationary disk begins to rotate. After 3 seconds, it is rotating at 60 rad/sec. What is the average angular acceleration?
dt
d
2s
rad
s
rad/s rad/s
t20
3
060
Demo: Atwood Machine
Physics 7B Lecture 718-Feb-2010 Slide 30 of 36
Angular Momentum
• Angular Momentum: Product of position vector and momentum vector
• Why is angular momentum important? Like energy and momentum, angular momentum is conserved.
12 LLL
prL
• Angular Impulse: Change in angular momentum vector
Physics 7B Lecture 718-Feb-2010 Slide 31 of 36
Angular Momentum
• What’s the angular momentum of a point particle?
p rprL sin
p
r┴
r
θ
Physics 7B Lecture 718-Feb-2010 Slide 32 of 36
Torque
• Which way will the scale tip?
• Rotation of scale is influenced by:– Magnitude of forces
– Location of forces
1 kg 1.5 kg 1 kg 1.5 kg
Physics 7B Lecture 718-Feb-2010 Slide 33 of 36
Torque
• Which is more effective?
• Rotation of wrench is influenced by:– Magnitude of forces
– Location of forces
– Direction of forces
F1 F2
F1
F2
Physics 7B Lecture 718-Feb-2010 Slide 34 of 36
Torque
• Torque: The cause or agent of angular acceleration
• The angular velocity of an object will not change unless acted upon by a torque
• The net torque on an object is equal to the rate of change of angular momentum
00
Object on Net
dt
LdObject on Net
Fr
Physics 7B Lecture 718-Feb-2010 Slide 35 of 36
Torque
• What’s the torque on a point particle?
F rFr sin
F
r┴
r
θ
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